TY - JOUR
T1 - Von Neumann Stability Analysis of Symplectic Integrators Applied to Hamiltonian PDEs
AU - Helen M. Regan
JO - Journal of Computational Mathematics
VL - 6
SP - 611
EP - 618
PY - 2002
DA - 2002/12
SN - 20
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8946.html
KW - symplectic integration, Hamiltonian PDEs, linear stability, von Neumann analysis.
AB - <p style="text-align: justify;">Symplectic integration of separable Hamiltonian ordinary and partial differential equations is discussed. A von Neumann analysis is performed to achieve general linear stability criteria for symplectic methods applied to a restricted class of Hamiltonian PDEs. In this treatment, the symplectic step is performed prior to the spatial step, as opposed to the spatial, as opposed to the standard approach of spatially discretising the PDE&nbsp;to form a system of Hamiltonian ODEs to which a symplectic integrator can be applied. In this way stability criteria are achieved by considering the spectra of linearised Hamiltonian PDEs rather than spatial step size.</p>